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A line segment is bisected by a line with the equation # 8 y + 5 x = 4 #. If one end of the line segment is at #( 2 , 7 )#, where is the other end?

Answer 1

Wyatt Anderson

#(-(442)/(89), -(369)/(89))#

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Answer 2

Ella Armstrong

To find the other end of the line segment bisected by the line with the equation (8y + 5x = 4), given one end at ((2, 7)), we can use the midpoint formula.

First, rearrange the equation of the line to solve for (y): [8y = -5x + 4] [y = -\frac{5}{8}x + \frac{1}{2}]

The midpoint formula is: [ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) ]

Given one end at ((2, 7)), let's denote the other end as ((x, y)). Using the midpoint formula, we equate the midpoint to ((2, 7)) and solve for (x) and (y): [ \frac{2 + x}{2} = 2 ] [ x + 2 = 4 ] [ x = 2 ]

[ \frac{7 + y}{2} = 7 ] [ 7 + y = 14 ] [ y = 7 ]

So, the other end of the line segment is at ((2, 7)).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.